Details

Time bar (total: 9.8s)

sample66.0ms

Algorithm
intervals
Results
25.0ms61×body1280valid
16.0ms65×body640valid
8.0ms28×body2560valid
5.0ms69×body80valid
3.0ms22×body320valid
1.0ms11×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
199
done99

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.4b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.2b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series318.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* x x) 1.0)
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
176.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify1.6s

Counts
65 → 65
Iterations

Useful iterations: 3 (612.0ms)

IterNodesCost
0141885
1332812
2912719
33250703
done5000703

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
115.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series309.0ms

Counts
2 → 6
Calls
2 calls:
164.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
145.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.5s

Counts
292 → 292
Iterations

Useful iterations: 2 (715.0ms)

IterNodesCost
03364436
18603460
230312955
done50002955

prune633.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.5b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.3b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+ div-inv
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
3.0ms
(/ 0.0625 (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
82.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
98.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 0.0625 (pow x 5))
43.0ms
(/ 0.125 (pow x 3))
185.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
56.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify894.0ms

Counts
172 → 172
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
03182936
16892663
220962511
done50002507

prune405.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.125 (pow x 3))
8.5b
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
40×times-frac
30×*-un-lft-identity
28×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
9×log-prod
8×add-exp-log
5×difference-of-squares sqr-pow
4×cube-mult log-div unpow3 add-cbrt-cube
3×pow1 div-exp associate-/l*
2×frac-sub add-log-exp
1×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ rem-log-exp pow-exp clear-num log-pow flip-- flip-+ div-inv distribute-lft-out--
Counts
2 → 87
Calls
2 calls:
4.0ms
(/ 0.125 (pow x 3))
34.0ms
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

series200.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ 0.125 (pow x 3))
158.0ms
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

simplify625.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (198.0ms)

IterNodesCost
02041459
14431276
213231216
done50001216

prune176.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.6b

bsearch82.0ms

Steps
ItersRangePoint
9
0.00016167321766412214
1766.3470775505596
0.8894030106629419
10
-3752817.331716861
-5.670122129476186e-07
-1.0108746280769982

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03557
14057
done4057

end0.0ms

sample1.9s

Algorithm
intervals
Results
954.0ms2299×body1280valid
380.0ms1555×body640valid
232.0ms822×body2560valid
115.0ms804×body320valid
69.0ms2139×body80valid
31.0ms381×body160valid